//----------------------------------------------------------------------------
bool HelixTubeSurface::MoveCamera ()
{
APoint position = mCurve->GetPosition(mCurveTime);
AVector tangent = mCurve->GetTangent(mCurveTime);
AVector binormal = tangent.UnitCross(AVector::UNIT_Z);
AVector normal = binormal.UnitCross(tangent);
mCamera->SetFrame(position, tangent, normal, binormal);
mCuller.ComputeVisibleSet(mScene);
return true;
}
//----------------------------------------------------------------------------
void AmbientRegionActor::_UpdateDirLightCamera()
{
AVector dir = AVector::AnglesToDirection(Mathf::DEG_TO_RAD*mHorAngle,
Mathf::DEG_TO_RAD*mVerAngle);
dir.Normalize();
Scene *scene = DynamicCast<Scene>(GetTopestParent());
if (scene)
{
EnvirParam *envirParam = scene->GetEnvirParam();
Light *lightDir = envirParam->GetLight_Dir();
Projector *projector = envirParam->GetLight_Dir_Projector();
lightDir->Ambient = Float4(mAmbientColor[0], mAmbientColor[1],
mAmbientColor[2], mIntensity);
lightDir->Intensity = mIntensity;
lightDir->Diffuse = Float4(mDiffuseColor[0], mDiffuseColor[1],
mDiffuseColor[2], 1.0f);
lightDir->Specular = Float4(mSpecularColor[0], mSpecularColor[1],
mSpecularColor[2], mSpecularPow);
float upDot = dir.Dot(-AVector::UNIT_Z);
if (upDot >= 0.99f)
{
}
else
{
AVector upTemp = AVector::UNIT_Z;
AVector right = dir.UnitCross(upTemp);
AVector up = right.UnitCross(dir);
lightDir->DVector = dir;
lightDir->UVector = up;
lightDir->RVector = right;
APoint camPos = mLightCameraLookPosition - dir*mLightCameraLookDistance;
projector->SetFrame(camPos, lightDir->DVector,
lightDir->UVector, lightDir->RVector);
}
if (!projector->IsPerspective())
{
projector->SetFrustum(0.1f, 100.0f,
-mLightCameraExtent, mLightCameraExtent, -mLightCameraExtent,
mLightCameraExtent);
}
else
{
projector->SetFrustum(mLightCameraExtent, 1.0f, 1.0f, 100.0f);
}
}
}
//----------------------------------------------------------------------------
void CameraActor::LookAt(const APoint &pos)
{
APoint localPos = LocalTransform.GetTranslate();
AVector dir = pos - localPos;
float length = dir.Normalize();
if (length > 0.0f)
{
AVector right = dir.UnitCross(AVector::UNIT_Z);
AVector up = right.UnitCross(dir);
LocalTransform.SetRotate(HMatrix(right, dir, up, AVector::ZERO, true));
}
}
//----------------------------------------------------------------------------
void PhysicsModule::GetData (APoint& center, HMatrix& incrRot) const
{
// Position is a point exactly on the hill.
APoint position;
position[0] = (float)(A1*mState[0]);
position[1] = (float)(A2*mState[2]);
position[2] = (float)(A3 - mState[0]*mState[0] - mState[2]*mState[2]);
// Lift this point off the hill in the normal direction by the radius of
// the ball so that the ball just touches the hill. The hill is
// implicitly specified by F(x,y,z) = z - [a3 - (x/a1)^2 - (y/a2)^2]
// where (x,y,z) is the position on the hill. The gradient of F is a
// normal vector, Grad(F) = (2*x/a1^2,2*y/a2^2,1).
AVector normal;
normal[0] = 2.0f*position[0]/(float)mAux[0];
normal[1] = 2.0f*position[1]/(float)mAux[1];
normal[2] = 1.0f;
normal.Normalize();
center = position + ((float)Radius)*normal;
// Let the ball rotate as it rolls down hill. The axis of rotation is
// the perpendicular to hill normal and ball velocity. The angle of
// rotation from the last position is A = speed*deltaTime/radius.
AVector velocity;
velocity[0] = (float)(A1*mState[1]);
velocity[1] = (float)(A1*mState[3]);
velocity[2] = -2.0f*(velocity[0]*(float)mState[0] +
velocity[1]*(float)mState[2]);
float speed = velocity.Normalize();
float angle = speed*((float)mDeltaTime)/((float)Radius);
AVector axis = normal.UnitCross(velocity);
incrRot = HMatrix(axis, angle);
}
//----------------------------------------------------------------------------
void SurfacePatch::GetFrame (float u, float v, APoint& position,
AVector& tangent0, AVector& tangent1, AVector& normal) const
{
position = P(u, v);
tangent0 = PU(u, v);
tangent1 = PV(u, v);
tangent0.Normalize();
normal = tangent0.UnitCross(tangent1);
// The normalized first derivatives are not necessarily orthogonal.
// Recompute T1 so that {T0,T1,N} is an orthonormal set.
tangent1 = normal.Cross(tangent0);
}
//----------------------------------------------------------------------------
void SurfacePatch::ComputePrincipalCurvatureInfo (float u, float v,
float& curv0, float& curv1, AVector& dir0, AVector& dir1)
{
// Tangents: T0 = dP/du = (x_u,y_u,z_u), T1 = dP/dv = (x_v,y_v,z_v)
// Normal: N = Cross(T0,T1)/Length(Cross(T0,T1))
// Metric Tensor: G = +- -+
// | Dot(T0,T0) Dot(T0,T1) |
// | Dot(T1,T0) Dot(T1,T1) |
// +- -+
//
// Curvature Tensor: B = +- -+
// | -Dot(N,T0_u) -Dot(N,T0_v) |
// | -Dot(N,T1_u) -Dot(N,T1_v) |
// +- -+
//
// Principal curvatures k are the generalized eigenvalues of
//
// Bw = kGw
//
// If k is a curvature and w=(a,b) is the corresponding solution to
// Bw = kGw, then the principal direction as a 3D vector is d = a*U+b*V.
//
// Let k1 and k2 be the principal curvatures. The mean curvature
// is (k1+k2)/2 and the Gaussian curvature is k1*k2.
// Compute the derivatives.
AVector derU = PU(u, v);
AVector derV = PV(u, v);
AVector derUU = PUU(u, v);
AVector derUV = PUV(u, v);
AVector derVV = PVV(u, v);
// Compute the metric tensor.
float metricTensor[2][2];
metricTensor[0][0] = derU.Dot(derU);
metricTensor[0][1] = derU.Dot(derV);
metricTensor[1][0] = metricTensor[0][1];
metricTensor[1][1] = derV.Dot(derV);
// Compute the curvature tensor.
AVector normal = derU.UnitCross(derV);
float curvatureTensor[2][2];
curvatureTensor[0][0] = -normal.Dot(derUU);
curvatureTensor[0][1] = -normal.Dot(derUV);
curvatureTensor[1][0] = curvatureTensor[0][1];
curvatureTensor[1][1] = -normal.Dot(derVV);
// Characteristic polynomial is 0 = det(B-kG) = c2*k^2+c1*k+c0.
float c0 = curvatureTensor[0][0]*curvatureTensor[1][1] -
curvatureTensor[0][1]*curvatureTensor[1][0];
float c1 = 2.0f*curvatureTensor[0][1]* metricTensor[0][1] -
curvatureTensor[0][0]*metricTensor[1][1] -
curvatureTensor[1][1]*metricTensor[0][0];
float c2 = metricTensor[0][0]*metricTensor[1][1] -
metricTensor[0][1]*metricTensor[1][0];
// Principal curvatures are roots of characteristic polynomial.
float temp = Mathf::Sqrt(Mathf::FAbs(c1*c1 - 4.0f*c0*c2));
curv0 = -0.5f*(c1+temp);
curv1 = 0.5f*(-c1+temp);
// Principal directions are solutions to (B-kG)w = 0,
// w1 = (b12-k1*g12,-(b11-k1*g11)) OR (b22-k1*g22,-(b12-k1*g12))
float a0 = curvatureTensor[0][1] - curv0*metricTensor[0][1];
float a1 = curv0*metricTensor[0][0] - curvatureTensor[0][0];
float length = Mathf::Sqrt(a0*a0 + a1*a1);
if (length >= Mathf::ZERO_TOLERANCE)
{
dir0 = a0*derU + a1*derV;
}
else
{
a0 = curvatureTensor[1][1] - curv0*metricTensor[1][1];
a1 = curv0*metricTensor[0][1] - curvatureTensor[0][1];
length = Mathf::Sqrt(a0*a0 + a1*a1);
if (length >= Mathf::ZERO_TOLERANCE)
{
dir0 = a0*derU + a1*derV;
}
else
{
// Umbilic (surface is locally sphere, any direction principal).
dir0 = derU;
}
}
dir0.Normalize();
// Second tangent is cross product of first tangent and normal.
dir1 = dir0.Cross(normal);
}
//----------------------------------------------------------------------------
void Triangles::UpdateModelTangentsUseTCoords (VertexBufferAccessor& vba)
{
// Each vertex can be visited multiple times, so compute the tangent
// space only on the first visit. Use the zero vector as a flag for the
// tangent vector not being computed.
const int numVertices = vba.GetNumVertices();
bool hasTangent = vba.HasTangent();
Float3 zero(0.0f, 0.0f, 0.0f);
int i;
if (hasTangent)
{
for (i = 0; i < numVertices; ++i)
{
vba.Tangent<Float3>(i) = zero;
}
}
else
{
for (i = 0; i < numVertices; ++i)
{
vba.Binormal<Float3>(i) = zero;
}
}
const int numTriangles = GetNumTriangles();
for (i = 0; i < numTriangles; i++)
{
// Get the triangle vertices' positions, normals, tangents, and
// texture coordinates.
int v0, v1, v2;
if (!GetTriangle(i, v0, v1, v2))
{
continue;
}
APoint locPosition[3] =
{
vba.Position<Float3>(v0),
vba.Position<Float3>(v1),
vba.Position<Float3>(v2)
};
AVector locNormal[3] =
{
vba.Normal<Float3>(v0),
vba.Normal<Float3>(v1),
vba.Normal<Float3>(v2)
};
AVector locTangent[3] =
{
(hasTangent ? vba.Tangent<Float3>(v0) : vba.Binormal<Float3>(v0)),
(hasTangent ? vba.Tangent<Float3>(v1) : vba.Binormal<Float3>(v1)),
(hasTangent ? vba.Tangent<Float3>(v2) : vba.Binormal<Float3>(v2))
};
Float2 locTCoord[3] =
{
vba.TCoord<Float2>(0, v0),
vba.TCoord<Float2>(0, v1),
vba.TCoord<Float2>(0, v2)
};
for (int curr = 0; curr < 3; ++curr)
{
Float3 currLocTangent = (Float3)locTangent[curr];
if (currLocTangent != zero)
{
// This vertex has already been visited.
continue;
}
// Compute the tangent space at the vertex.
AVector norvec = locNormal[curr];
int prev = ((curr + 2) % 3);
int next = ((curr + 1) % 3);
AVector tanvec = ComputeTangent(
locPosition[curr], locTCoord[curr],
locPosition[next], locTCoord[next],
locPosition[prev], locTCoord[prev]);
// Project T into the tangent plane by projecting out the surface
// normal N, and then making it unit length.
tanvec -= norvec.Dot(tanvec)*norvec;
tanvec.Normalize();
// Compute the bitangent B, another tangent perpendicular to T.
AVector binvec = norvec.UnitCross(tanvec);
if (vba.HasTangent())
{
locTangent[curr] = tanvec;
if (vba.HasBinormal())
{
vba.Binormal<Float3>(curr) = binvec;
}
}
else
{
vba.Binormal<Float3>(curr) = tanvec;
}
}
}
}